Vassilios Tsiantos

Scalable parallel micromagnetic solvers for magnetic nanostructures

A parallel finite element micromagnetics package has been implemented, that is highly scalable, easily portable and combines different solvers for the micromagnetic equations. The implementation is based on the standard Galerkin discretization on tetrahedral meshes with linear basis functions. A static energy minimization, a dynamic time integration, and the nudged elastic band method have been implemented. The details of the implementation and some aspects of the optimization are discussed and timing and speedup results are given. Nucleation and magnetization reversal processes in permalloy nanodots are investigated with this micromagnetics package.

Time resolved micromagnetics using a preconditioned time integration method

A detailed description for the solution of the Landau–Lifshitz–Gilbert equation with the finite element method is given. The use of implicit time integration schemes with proper preconditioning is reported. Simulations of a single-phase magnetic nanoelement without surface roughness and a magnetic nanoelement with a granular structure are performed to investigate the influence of the microstructure on the numerical behavior. Nanoelements with a granular structure cause an inhomogeneous computational grid. In granular systems preconditioning for time integration speeds up the simulations by three orders of magnitude as compared to conventional time integration schemes like the Adams method. r 2002 Elsevier Science B.V. All rights reserved.

Domain wall motion in nanowires using moving grids (invited)

The magnetization reversal process of Co nanowires was investigated using a moving mesh technique. The nucleation and expansion of reversed domains is calculated by solving the Gilbert equation of motion for different damping constants. The adaptive finite element method reduces the total CPU time by more than a factor of 4 as compared to a uniform mesh. Two different domain wall types are observed. For a wire diameter of d=10 nm transverse walls occur and gyromagnetic precession limits the domain wall velocity. The domain wall velocity increases from 50 to 520 m/s as the Gilbert damping constant increases from α=0.05 to α=1 at an applied field of 500 kA/m. For a diameter greater than 20 nm vortex walls are formed. The vortex mobility increases with decreasing damping constant. Thus velocities up to 2000 m/s are reached for a wire diameter of 40 nm, α=0.05, and an applied field of 250 kA/m.

Magnetization reversal in granular nanowires

The switching process of granular Co nanowires is investigated using the finite element method. The wires have a diameter of 55 nm and a length of 1000 nm. Transmission electron microscopy (TEM) investigations show two different types of hcp-structured grains. For one, the c axis is randomly oriented in a plane perpendicular to the long axis of the wire, and the other has the c axis parallel to the long axis. The numerical results show that finite element micromagnetics can explain the influence of the microstructure in magnetic nanosystems.

The effect of the cell size in Langevin micromagnetic simulations

Abstract Langevin micromagnetics treats finite temperature effects by adding a thermal fluctuation field, Hth, to the effective field. If combined with the finite element method or the finite difference method, the spatial correlation length of the random field is usually taken to be equal to the cell size of the computational grid. The influence of the cell size has been studied for two different systems: a system close to equilibrium and a system which exhibits thermal activated switching. The results suggest that the calculated properties are independent of the cell size if the cell size is smaller than the thermal exchange length A/(J s H th ) . The term A is the exchange constant and Js is the spontaneous magnetic polarization. Below this critical length the magnetization is uniform.

Micromagnetic simulation of the pinning and depinning process in permanent magnets

We have studied the pinning of magnetic domain walls on a simplified model of the cell structure of Sm(Co,Fe,Cu,Zr)/sub z/ precipitation hardened magnets. The pinning field strongly depends on the thickness of the intercellular phase if it is smaller than the domain wall width. Its maximum value has been verified with a one-dimensional analytical model. The cell structure plays an important role in the depinning process and it has been found that the pinning field depends linearly on the relative thickness of the intercellular phase. This behavior is universal for attractive and repulsive pinning.

Finite element simulation of discrete media with granular structure

Summary form only given. Discrete media show great potential for future ultra-high density magnetic recording. A possible patterning scheme is the removal of magnetic material from existing media using a focused ion beam. Patterning significantly changes the hysteresis properties. In this work we apply a hybrid finite element/boundary element method to simulate the magnetization reversal process in a perpendicular granular film, a patterned media, and a single magnetic island. We start with a continuous CoCrPt film consisting of 625 columnar grains which are obtained from a Voronoi tesselation. The grain diameter is 10 nm and the film thickness is 21 nm. In a second step, we take out elements in a grid pattern, to obtain an array of individual islands. The island size is 70 nm with a gap of 20 nm. The subsequent calculation of equilibrium states solving the Gilbert equation of motion provides the demagnetization curve.

Ultrafast switching of magnetic nanoelements using a rotating field

Nanostructured granular Ni80Fe20 and Co films are studied using a 3D hybrid finite element/boundary element model. Switching dynamics are calculated for external fields applied unidirectional after a rise time of 0.1 ns and for a 10 GHz rotational field with a field strength of Hext=0.2 Js/μ0 (160 kA/m for NiFe and 280 kA/m for Co). The transient magnetization patterns show that reversal in the unidirectional field proceeds by the nucleation and propagation of end domains towards the center of the element. The switching time strongly depends on the Gilbert damping parameter α. Materials with uniaxial anisotropy (Co), require larger field, but exhibit shorter switching times. Reversal in rotational fields involves inhomogeneous rotation of the end domains towards the rotational field direction leading to partial flux-closure structures. Shorter switching times are obtained by the application of the 10 GHz rotational field (tsw=0.05 ns). Precessional oscillation effects after abruptly switching off the exte...

Micromagnetic Simulation of Switching Events

Magnetic switching of small particles, thin film elements and magnetic nanowires becomes increasingly important in magnetic storage and magneto electronic devices. Micromagnetic switching events are studied using a hybrid finite element / boundary element method. The space discretization of the Gilbert equation leads to a system of ordinary differential equations. Its numerical integration provides the time evolution of the magnetization under the influence of an external field. Thermal fluctuations may be treated by a random field. The reversal mode drastically depends on the Gilbert damping constant. Decreasing the damping constant from α = 1 to α ≤ 0.1 changes the reversal mode from uniform rotation to inhomogeneous switching. The decrease of the damping leads to the formation of vortices in circular nanodots and to a nucleation process in columnar grains. Elongated Co particles reverse by rotation if the length of the particle is smaller than 25nm. Irreversible switching of longer particles occurs due to the formation of a nucleus of reversed magnetization and successive domain wall motion.

Stiffness analysis for the micromagnetic standard problem No. 4

In this article solutions to micromagnetic standard problem No. 4, a 500-nm3125-nm-wide NiFe film, are presented. A three-dimensional-finite element simulation based on the solution of the Gilbert equation has been used. The simulations show that two different reversal mechanisms occur for the two different applied fields. For a field at 170° counterclockwise from the saturation direction there is a nonuniform rotation of magnetization towards the direction of the applied field, with the magnetization at the ends rotating faster than the magnetization in the center. For a field at 190° counterclockwise from the saturation direction the magnetization at the ends and in the center rotate in opposite directions leading to the formation of a 360° wall after 0.22 ns associated with a peak in the exchange energy. Moreover, the time for the magnetization component parallel to the long axis to cross the zero is 0.136 and 0.135 ns for field 1 and field 2, respectively. The stiffness of the problem has been investigated solving the system of ordinary differential equations with a nonstiff method ~Adams! and a stiff one ~backward differentiation formula, BDF!. For the measure of stiffness the ratio of the total number of time steps ~nst! taken by the two solvers, that is nst~Adams!/ nst~BDF!, has been used. This ratio is 0.784 for field 1 and 0.593 for field 2, which means that the nonstiff method ~Adams! uses larger time steps than the stiff method ~BDF! and consequently the systems are not stiff. The average time step for the Adams method was 0.2 ps for both fields.